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68-466: (Redirected from DoF ) DOF may stand for: Science [ edit ] Depth of field , in photography a measurement of depth of acceptable sharpness in the object space, or subject space Depth of focus , in lens optics describes the tolerance of placement of the image plane to the lens Digital obstacle file , in aviation contains data on man-made obstacles 2,5-Dimethoxy-4-fluoroamphetamine (DOF),

136-779: A different equivalent thin lens that is totally in air, with focal length equal to the eye's EFL. For the case of a lens of thickness d in air ( n 1 = n 2 = 1 ), and surfaces with radii of curvature R 1 and R 2 , the effective focal length f is given by the Lensmaker's equation : 1 f = ( n − 1 ) ( 1 R 1 − 1 R 2 + ( n − 1 ) d n R 1 R 2 ) , {\displaystyle {\frac {1}{f}}=(n-1)\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}+{\frac {(n-1)d}{nR_{1}R_{2}}}\right),} where n

204-460: A focus , or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power. In most photography and all telescopy , where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and

272-403: A normal lens for a 35 mm camera with a focal length of f = 50 mm. To focus a distant object ( s 1 ≈ ∞ ), the rear principal plane of the lens must be located a distance s 2 = 50 mm from the film plane, so that it is at the location of the image plane. To focus an object 1 m away ( s 1 = 1,000 mm), the lens must be moved 2.6 mm farther away from

340-471: A photographic lens or a telescope ), there are several related concepts that are referred to as focal lengths: For an optical system in air the effective focal length, front focal length, and rear focal length are all the same and may be called simply "focal length". For an optical system in a medium other than air or vacuum, the front and rear focal lengths are equal to the EFL times the refractive index of

408-512: A psychedelic drug . Distance-of-Flight , a mass spectrometry technology. Degrees of freedom , used in mechanics , statistics , as well as physics and chemistry . Music [ edit ] Deeds of Flesh , a Death Metal band Deutsch-Österreichisches Feingefühl or DÖF, a 1980s Austrian-German Neue Deutsche Welle pop band. Other [ edit ] Dansk Ornitologisk Forening , Danish Ornithological Society Department of Finance (Philippines) , an executive department in

476-450: A combination of lens design and post-processing: Wavefront coding is a method by which controlled aberrations are added to the optical system so that the focus and depth of field can be improved later in the process. The lens design can be changed even more: in colour apodization the lens is modified such that each colour channel has a different lens aperture. For example, the red channel may be f /2.4 , green may be f /2.4 , whilst

544-597: A convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so f = − R 2 , {\displaystyle f=-{R \over 2},} where R is the radius of curvature of the mirror's surface. See Radius of curvature (optics) for more information on the sign convention for radius of curvature used here. Camera lens focal lengths are usually specified in millimetres (mm), but some older lenses are marked in centimetres (cm) or inches. Focal length ( f ) and field of view (FOV) of

612-603: A detail at distance x d from the subject can be expressed as a function of the subject magnification m s , focal length f , f-number N , or alternatively the aperture d , according to b = f m s N x d s ± x d = d m s x d D . {\displaystyle b={\frac {fm_{\mathrm {s} }}{N}}{\frac {x_{\mathrm {d} }}{s\pm x_{\mathrm {d} }}}=dm_{\mathrm {s} }{\frac {x_{\mathrm {d} }}{D}}.} The minus sign applies to

680-401: A different field of view. If the focal length is altered to maintain the field of view, while holding the f-number constant , the change in focal length will counter the decrease of DOF from the smaller sensor and increase the depth of field (also by the crop factor). However, if the focal length is altered to maintain the field of view, while holding the aperture diameter constant ,

748-417: A distant light source on a screen. The lens is moved until a sharp image is formed on the screen. In this case ⁠ 1 / u ⁠ is negligible, and the focal length is then given by Determining the focal length of a concave lens is somewhat more difficult. The focal length of such a lens is defined as the point at which the spreading beams of light meet when they are extended backwards. No image

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816-444: A foreground object, and the plus sign applies to a background object. The blur increases with the distance from the subject; when b is less than the circle of confusion, the detail is within the depth of field. Focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light ; it is the inverse of the system's optical power . A positive focal length indicates that

884-617: A given angle of view, by a factor known as the crop factor . The optical power of a lens or curved mirror is a physical quantity equal to the reciprocal of the focal length, expressed in metres . A dioptre is its unit of measurement with dimension of reciprocal length , equivalent to one reciprocal metre , 1 dioptre = 1 m . For example, a 2-dioptre lens brings parallel rays of light to focus at 1 ⁄ 2 metre. A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge. The main benefit of using optical power rather than focal length

952-516: A glass for serving "lowball" cocktails that is typically 12-16 fluid ounces (350-470ml) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title DOF . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=DOF&oldid=1225090207 " Category : Disambiguation pages Hidden categories: Short description

1020-448: A greater (or less, if so desired) apparent depth of field than any of the individual source images. Similarly, in order to reconstruct the 3-dimensional shape of an object, a depth map can be generated from multiple photographs with different depths of field. Xiong and Shafer concluded, in part, "...   the improvements on precisions of focus ranging and defocus ranging can lead to efficient shape recovery methods." Another approach

1088-403: A lens are inversely proportional. For a standard rectilinear lens , F O V = 2 arctan ⁡ ( x 2 f ) {\textstyle \mathrm {FOV} =2\arctan {\left({x \over 2f}\right)}} , where x is the width of the film or imaging sensor. When a photographic lens is set to "infinity", its rear principal plane is separated from

1156-459: A lens focused at an object whose distance from the lens is at the hyperfocal distance H will hold a depth of field from H /2 to infinity, if the lens is focused to H /2 , the depth of field will be from H /3 to H ; if the lens is then focused to H /3 , the depth of field will be from H /4 to H /2 , etc. Thomas Sutton and George Dawson first wrote about hyperfocal distance (or "focal range") in 1867. Louis Derr in 1906 may have been

1224-458: A lens; at that distance, a point object will produce a small spot image. Otherwise, a point object will produce a larger or blur spot image that is typically and approximately a circle. When this circular spot is sufficiently small, it is visually indistinguishable from a point, and appears to be in focus. The diameter of the largest circle that is indistinguishable from a point is known as the acceptable circle of confusion , or informally, simply as

1292-404: A narrower angle of view ; conversely, shorter focal length or higher optical power is associated with lower magnification and a wider angle of view. On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length (higher optical power) leads to higher magnification because the subject can be brought closer to

1360-536: A scene, so the focus and depth of field can be altered after the photo is taken. Diffraction causes images to lose sharpness at high f-numbers (i.e., narrow aperture stop opening sizes), and hence limits the potential depth of field. (This effect is not considered in the above formula giving approximate DOF values.) In general photography this is rarely an issue; because large f-numbers typically require long exposure times to acquire acceptable image brightness, motion blur may cause greater loss of sharpness than

1428-428: A single aperture setting for interiors (e.g., scenes inside a building) and another for exteriors (e.g., scenes in an area outside a building), and adjust exposure through the use of camera filters or light levels. Aperture settings are adjusted more frequently in still photography, where variations in depth of field are used to produce a variety of special effects. Precise focus is only possible at an exact distance from

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1496-399: A system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to

1564-483: A thin light plane across the subject that is mounted on a moving stage perpendicular to the light plane. This ensures the entire subject remains in sharp focus from the nearest to the farthest details, providing comprehensive depth of field in a single image. Initially developed in the 1960s and further refined in the 1980s and 1990s, LSP was particularly valuable in scientific and biomedical photography before digital focus stacking became prevalent. Other technologies use

1632-450: Is a distance from a lens beyond which all objects can be brought into an "acceptable" focus . As the hyperfocal distance is the focus distance giving the maximum depth of field, it is the most desirable distance to set the focus of a fixed-focus camera . The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable. The hyperfocal distance has a property called "consecutive depths of field", where

1700-413: Is called "the focal length" of the system. Some modern authors avoid this ambiguity by instead defining "focal length" to be a synonym for EFL. The distinction between front/rear focal length and EFL is important for studying the human eye. The eye can be represented by an equivalent thin lens at an air/fluid boundary with front and rear focal lengths equal to those of the eye, or it can be represented by

1768-507: Is different from Wikidata All article disambiguation pages All disambiguation pages Depth of field For cameras that can only focus on one object distance at a time, depth of field is the distance between the nearest and the farthest objects that are in acceptably sharp focus in the image. "Acceptably sharp focus" is defined using a property called the " circle of confusion ". The depth of field can be determined by focal length , distance to subject (object to be imaged),

1836-592: Is focus sweep. The focal plane is swept across the entire relevant range during a single exposure. This creates a blurred image, but with a convolution kernel that is nearly independent of object depth, so that the blur is almost entirely removed after computational deconvolution. This has the added benefit of dramatically reducing motion blur. Light Scanning Photomacrography (LSP) is another technique used to overcome depth of field limitations in macro and micro photography. This method allows for high-magnification imaging with exceptional depth of field. LSP involves scanning

1904-403: Is formed during such a test, and the focal length must be determined by passing light (for example, the light of a laser beam) through the lens, examining how much that light becomes dispersed/ bent, and following the beam of light backwards to the lens's focal point. For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses or mirrors (e.g.

1972-413: Is negative and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens. When a lens is used to form an image of some object, the distance from the object to the lens u , the distance from the lens to the image v , and the focal length f are related by The focal length of a thin convex lens can be easily measured by using it to form an image of

2040-418: Is negative if the second surface is convex, and positive if concave. Sign conventions vary between different authors, which results in different forms of these equations depending on the convention used. For a spherically-curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is positive for a concave mirror, and negative for

2108-461: Is often referred to as a wide-angle lens (typically 35 mm and less, for 35 mm-format cameras), while a lens significantly longer than normal may be referred to as a telephoto lens (typically 85 mm and more, for 35 mm-format cameras). Technically, long focal length lenses are only "telephoto" if the focal length is longer than the physical length of the lens, but the term is often used to describe any long focal length lens. Due to

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2176-586: Is paramount. Other authors such as Ansel Adams have taken the opposite position, maintaining that slight unsharpness in foreground objects is usually more disturbing than slight unsharpness in distant parts of a scene. Some methods and equipment allow altering the apparent DOF , and some even allow the DOF to be determined after the image is made. These are based or supported by computational imaging processes. For example, focus stacking combines multiple images focused on different planes, resulting in an image with

2244-421: Is the transverse magnification which is the ratio of the lateral image size to the lateral subject size. Image sensor size affects DOF in counterintuitive ways. Because the circle of confusion is directly tied to the sensor size, decreasing the size of the sensor while holding focal length and aperture constant will decrease the depth of field (by the crop factor). The resulting image however will have

2312-416: Is the refractive index of the lens medium. The quantity ⁠ 1 / f ⁠ is also known as the optical power of the lens. The corresponding front focal distance is: FFD = f ( 1 + ( n − 1 ) d n R 2 ) , {\displaystyle {\mbox{FFD}}=f\left(1+{\frac {(n-1)d}{nR_{2}}}\right),} and

2380-459: The DOF will remain constant. For a given subject framing and camera position, the DOF is controlled by the lens aperture diameter, which is usually specified as the f-number (the ratio of lens focal length to aperture diameter). Reducing the aperture diameter (increasing the f-number ) increases the DOF because only the light travelling at shallower angles passes through the aperture so only cones of rays with shallower angles reach

2448-425: The f-number that will give the maximum possible sharpness; Peterson's approach determines the minimum f-number that will give the desired sharpness in the final image and yields a maximum depth of field for which the desired sharpness can be achieved. In combination, the two methods can be regarded as giving a maximum and minimum f-number for a given situation, with the photographer free to choose any value within

2516-482: The hyperfocal distance , sometimes almost at infinity. For example, if photographing a cityscape with a traffic bollard in the foreground, this approach, termed the object field method by Merklinger, would recommend focusing very close to infinity, and stopping down to make the bollard sharp enough. With this approach, foreground objects cannot always be made perfectly sharp, but the loss of sharpness in near objects may be acceptable if recognizability of distant objects

2584-549: The 1800s and are still in use today on view cameras, technical cameras, cameras with tilt/shift or perspective control lenses, etc. Swiveling the lens or sensor causes the plane of focus (POF) to swivel, and also causes the field of acceptable focus to swivel with the POF ; and depending on the DOF criteria, to also change the shape of the field of acceptable focus. While calculations for DOF of cameras with swivel set to zero have been discussed, formulated, and documented since before

2652-539: The 1940s, documenting calculations for cameras with non-zero swivel seem to have begun in 1990. More so than in the case of the zero swivel camera, there are various methods to form criteria and set up calculations for DOF when swivel is non-zero. There is a gradual reduction of clarity in objects as they move away from the POF , and at some virtual flat or curved surface the reduced clarity becomes unacceptable. Some photographers do calculations or use tables, some use markings on their equipment, some judge by previewing

2720-804: The Philippines Department of Finance (Northern Ireland) , a government department in Northern Ireland Diario Oficial de la Federación (Official Journal of the Federation), published by the Mexican government DOF ASA , company DOF Subsea , company Documento de Origem Florestal (Forest Origin Document), a governmental Brazilian system to regulation of extraction, transport and commerce of native forest products. Double old fashioned glass ,

2788-512: The acceptable circle of confusion size, and aperture. Limitations of depth of field can sometimes be overcome with various techniques and equipment. The approximate depth of field can be given by: DOF ≈ 2 u 2 N c f 2 {\displaystyle {\text{DOF}}\approx {\frac {2u^{2}Nc}{f^{2}}}} for a given maximum acceptable circle of confusion c , focal length f , f-number N , and distance to subject u . As distance or

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2856-402: The angle subtended by a large-enough print viewed at a typical viewing distance of the print diagonal, which therefore yields a normal perspective when viewing the print; this angle of view is about 53 degrees diagonally. For full-frame 35 mm-format cameras, the diagonal is 43 mm and a typical "normal" lens has a 50 mm focal length. A lens with a focal length shorter than normal

2924-429: The back focal distance: BFD = f ( 1 − ( n − 1 ) d n R 1 ) . {\displaystyle {\mbox{BFD}}=f\left(1-{\frac {(n-1)d}{nR_{1}}}\right).} In the sign convention used here, the value of R 1 will be positive if the first lens surface is convex, and negative if it is concave. The value of R 2

2992-444: The blue channel may be f /5.6 . Therefore, the blue channel will have a greater depth of field than the other colours. The image processing identifies blurred regions in the red and green channels and in these regions copies the sharper edge data from the blue channel. The result is an image that combines the best features from the different f-numbers . At the extreme, a plenoptic camera captures 4D light field information about

3060-413: The center of projection. For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points ) of the lens. For a converging lens (for example a convex lens ), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens ), the focal length

3128-442: The circle of confusion. The acceptable circle of confusion depends on how the final image will be used. The circle of confusion as 0.25 mm for an image viewed from 25 cm away is generally accepted. For 35   mm motion pictures, the image area on the film is roughly 22 mm by 16 mm. The limit of tolerable error was traditionally set at 0.05 mm (0.0020 in) diameter, while for 16 mm film , where

3196-444: The combined effects using the modulation transfer function . Many lenses include scales that indicate the DOF for a given focus distance and f-number ; the 35 mm lens in the image is typical. That lens includes distance scales in feet and meters; when a marked distance is set opposite the large white index mark, the focus is set to that distance. The DOF scale below the distance scales includes markings on either side of

3264-409: The difference v N − v F as the focus spread . If a subject is at distance s and the foreground or background is at distance D , let the distance between the subject and the foreground or background be indicated by x d = | D − s | . {\displaystyle x_{\mathrm {d} }=|D-s|.} The blur disk diameter b of

3332-457: The distance from the front principal plane to the object to photograph s 1 , and the distance from the rear principal plane to the image plane s 2 are then related by: 1 s 1 + 1 s 2 = 1 f . {\displaystyle {\frac {1}{s_{1}}}+{\frac {1}{s_{2}}}={\frac {1}{f}}\,.} As s 1 is decreased, s 2 must be increased. For example, consider

3400-582: The effective absolute aperture diameter can be used for similar formula in certain circumstances. Moreover, traditional depth-of-field formulas assume equal acceptable circles of confusion for near and far objects. Merklinger suggested that distant objects often need to be much sharper to be clearly recognizable, whereas closer objects, being larger on the film, do not need to be so sharp. The loss of detail in distant objects may be particularly noticeable with extreme enlargements. Achieving this additional sharpness in distant objects usually requires focusing beyond

3468-440: The film plane, to s 2 = 52.6 mm. The focal length of a lens determines the magnification at which it images distant objects. It is equal to the distance between the image plane and a pinhole that images distant objects the same size as the lens in question. For rectilinear lenses (that is, with no image distortion ), the imaging of distant objects is well modelled as a pinhole camera model . This model leads to

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3536-505: The first to derive a formula for hyperfocal distance. Rudolf Kingslake wrote in 1951 about the two methods of measuring hyperfocal distance. The DOF beyond the subject is always greater than the DOF in front of the subject. When the subject is at the hyperfocal distance or beyond, the far DOF is infinite, so the ratio is 1:∞; as the subject distance decreases, near:far DOF ratio increases, approaching unity at high magnification. For large apertures at typical portrait distances,

3604-719: The focal length. As a result, photos taken at extremely close range (i.e., so small u ) have a proportionally much smaller depth of field. Rearranging the DOF equation shows that it is the ratio between distance and focal length that affects DOF ; DOF ≈ 2 N c ( u f ) 2 = 2 N c ( 1 − 1 M T ) 2 {\displaystyle {\text{DOF}}\approx 2Nc\left({\frac {u}{f}}\right)^{2}=2Nc\left(1-{\frac {1}{M_{T}}}\right)^{2}} Note that M T = − f u − f {\textstyle M_{T}=-{\frac {f}{u-f}}}

3672-407: The image plane. In other words, the circles of confusion are reduced or increasing the DOF . For a given size of the subject's image in the focal plane, the same f-number on any focal length lens will give the same depth of field. This is evident from the above DOF equation by noting that the ratio u / f is constant for constant image size. For example, if the focal length is doubled,

3740-450: The image. When the POF is rotated, the near and far limits of DOF may be thought of as wedge-shaped, with the apex of the wedge nearest the camera; or they may be thought of as parallel to the POF . Traditional depth-of-field formulas can be hard to use in practice. As an alternative, the same effective calculation can be done without regard to the focal length and f-number . Moritz von Rohr and later Merklinger observe that

3808-451: The index that correspond to f-numbers . When the lens is set to a given f-number , the DOF extends between the distances that align with the f-number markings. Photographers can use the lens scales to work backwards from the desired depth of field to find the necessary focus distance and aperture. For the 35 mm lens shown, if it were desired for the DOF to extend from 1 m to 2 m, focus would be set so that index mark

3876-413: The loss from diffraction. However, diffraction is a greater issue in close-up photography, and the overall image sharpness can be degraded as photographers are trying to maximize depth of field with very small apertures. Hansma and Peterson have discussed determining the combined effects of defocus and diffraction using a root-square combination of the individual blur spots. Hansma's approach determines

3944-436: The medium in front of or behind the lens ( n 1 and n 2 in the diagram above). The term "focal length" by itself is ambiguous in this case. The historical usage was to define the "focal length" as the EFL times the index of refraction of the medium. For a system with different media on both sides, such as the human eye, the front and rear focal lengths are not equal to one another, and convention may dictate which one

4012-490: The popularity of the 35 mm standard , camera–lens combinations are often described in terms of their 35 mm-equivalent focal length, that is, the focal length of a lens that would have the same angle of view, or field of view, if used on a full-frame 35 mm camera. Use of a 35 mm-equivalent focal length is particularly common with digital cameras , which often use sensors smaller than 35 mm film, and so require correspondingly shorter focal lengths to achieve

4080-441: The range, as conditions (e.g., potential motion blur) permit. Gibson gives a similar discussion, additionally considering blurring effects of camera lens aberrations, enlarging lens diffraction and aberrations, the negative emulsion, and the printing paper. Couzin gave a formula essentially the same as Hansma's for optimal f-number , but did not discuss its derivation. Hopkins, Stokseth, and Williams and Becklund have discussed

4148-425: The ratio is still close to 1:1. This section covers some additional formula for evaluating depth of field; however they are all subject to significant simplifying assumptions: for example, they assume the paraxial approximation of Gaussian optics . They are suitable for practical photography, lens designers would use significantly more complex ones. For given near and far DOF limits D N and D F ,

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4216-487: The required f-number is smallest when focus is set to s = 2 D N D F D N + D F , {\displaystyle s={\frac {2D_{\mathrm {N} }D_{\mathrm {F} }}{D_{\mathrm {N} }+D_{\mathrm {F} }}},} the harmonic mean of the near and far distances. In practice, this is equivalent to the arithmetic mean for shallow depths of field. Sometimes, view camera users refer to

4284-407: The sensor or film, which is then situated at the focal plane , by the lens's focal length. Objects far away from the camera then produce sharp images on the sensor or film, which is also at the image plane. To render closer objects in sharp focus, the lens must be adjusted to increase the distance between the rear principal plane and the film, to put the film at the image plane. The focal length f ,

4352-402: The simple geometric model that photographers use for computing the angle of view of a camera; in this case, the angle of view depends only on the ratio of focal length to film size . In general, the angle of view depends also on the distortion. A lens with a focal length about equal to the diagonal size of the film or sensor format is known as a normal lens ; its angle of view is similar to

4420-399: The size is about half as large, the tolerance is stricter, 0.025 mm (0.00098 in). More modern practice for 35 mm productions set the circle of confusion limit at 0.025 mm (0.00098 in). The term "camera movements" refers to swivel (swing and tilt, in modern terminology) and shift adjustments of the lens holder and the film holder. These features have been in use since

4488-408: The size of the acceptable circle of confusion increases, the depth of field increases; however, increasing the size of the aperture (i.e., reducing f-number ) or increasing the focal length reduces the depth of field. Depth of field changes linearly with f-number and circle of confusion, but changes in proportion to the square of the distance to the subject and inversely in proportion to the square of

4556-418: The subject distance is also doubled to keep the subject image size the same. This observation contrasts with the common notion that "focal length is twice as important to defocus as f/stop", which applies to a constant subject distance, as opposed to constant image size. Motion pictures make limited use of aperture control; to produce a consistent image quality from shot to shot, cinematographers usually choose

4624-421: Was centered between the marks for those distances, and the aperture would be set to f /11 . On a view camera, the focus and f-number can be obtained by measuring the depth of field and performing simple calculations. Some view cameras include DOF calculators that indicate focus and f-number without the need for any calculations by the photographer. In optics and photography , hyperfocal distance

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